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arXiv · 2510.04989

Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations

Bo Peng
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Abstract

We show that the isomorphism of ergodic measure-preserving transformations is not Borel reducible to the relation induced by the conjugacy action of the full group of an ergodic measure-preserving transformation on itself. This answers a question of Le Ma\^{i}tre in the negative and gives a positive indication towards a conjecture of Sabok. In fact, we prove that the isomorphism of ergodic measure-preserving transformation is unbalanced, which answers another question of Le Ma\^{i}tre in the positive.

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Bo Peng. 2025-10-06. Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations. https://arxiv.org/abs/2510.04989

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